SALT LAKE CITY -- A federal judge has struck down parts of Utah’s anti-polygamy law as unconstitutional in a case brought by a polygamous star of a reality-television series. Months after the Supreme Court bolstered rights of same-sex couples, the Utah case could open a new frontier in the nation’s recognition of once-prohibited relationships.

Judge Clark Waddoups of U.S. District Court in Utah ruled late Friday that part of the state’s law prohibiting “cohabitation” — the language used in the law to restrict polygamous relationships — violated the First Amendment guarantee of free exercise of religion, as well as constitutional due process. He left standing the state’s ability to prohibit multiple marriages “in the literal sense” of having two or more valid marriage licenses.

The challenge to the law was brought by Kody Brown, who, along with his four wives and 17 children, stars in the show Sister Wives. The family argued that the state’s prohibition on cohabitation violated its rights to privacy and religious freedom. The Browns are members of the Apostolic United Brethren Church, a fundamentalist offshoot of the Mormon Church, which gave up polygamy around 1890 as Utah was seeking statehood.